Economic definition of true love
Current Availability
I'm afraid that Ed is currently unavailable for dating at this time. Exceptions to this can be made if you have a Math(s) Ph.D.
That said, if you genuinely believe:
- [math]p\left(You \cap The\,One \ne \{\empty\}\,|\,First\,Glance\right) \gg 0[/math]
then please stop by my office (F533) at the Haas School of Business (map) at your earliest convenience.
Future Availability
Please check back for updates.
True Love
Definition
Let [math]H[/math] denote the set of all entities (perhaps Humans, though we might also include dogs, cats and horses, according to historical precedent).
Let [math]T[/math] denote the set of pairs of individuals who have True Love, such that:
- [math]\forall\{i,j\} \in T: \quad (i \succ_j h \quad \forall h \ne i) \and (j \succ_i h \quad \forall h \ne j), \quad h \in H \cap \{\emptyset\}[/math]
Note that:
- The definition employs strict preferences. A polyamorous definition might allow weak preferences instead.
- The union with the empty set allows for people who would rather be alone (e.g. Tiny Fey), provided that we allow a mild abuse of notation so that [math]i \succ_{\{\emptyset\}} h[/math]. The inclusion of the empty set is not necessary with weak preferences as then we can allow [math] i \succsim_i i[/math] without violating the definition of the preference relation.
The Existance of True Love
Can we prove that [math] T \ne \{\emptyset\}\lt math\gt ? ====The Brad Pitt Problem==== Rational preferences aren't sufficient to guarantee that \lt math\gt T \ne \{\emptyset\}\lt math\gt . Recall that a preference relation is rational if it is complete and transitive: #Completeness: \lt math\gt \forall x,y \in X: \quad x \succsim y \;\or\; y \succsim x[/math]
- Transitivity: [math]\forall x,y,z \in X: \quad \mbox{if}\; \quad x \succsim y \;\and\; y \succsim x \;\mbox{then}\; x \succsim z[/math]
Also recall the definition of the strict preference relation:
- [math]x \succ y \quad \Leftrightarrow \quad \quad x \succsim y \;\and\; y \nsuccsim x[/math]
